In a radio communication system, the information bits are modulated at a transmitter end and consequently need to be demodulated at a receiver end. Thus, a radio receiver always has a RF (Radio Frequency) demodulation module. Basically, the RF demodulation module function consists of removing the carrier frequency from a received radio signal in order to recover a baseband signal. To perform this operation, a local oscillator part of the RF demodulation module, generates a frequency tone that ideally should be identical to the carrier frequency. The local oscillator should oscillate at the same frequency as the carrier frequency. Unfortunately, for several reasons (for instance the temperature variations) this local oscillator can drift. As a consequence, an oscillator frequency offset f0 appears between the carrier frequency and the oscillation frequency of the local oscillator. This frequency offset causes a significant degradation of the overall performance of the receiver.
An existing solution is, therefore, to estimate offset f0 and then to correct it.
For example, to this end, UMTS (Universal Mobile Telecommunications Systems) radio communication systems have common downlink physical channels P-CPICH (Primary Common Pilot Channel) and S-CPICH (Secondary Common Pilot Channel). Both CPICHs are fixed rate (30 kbits/s) downlink physical channels that carry a pre-defined bit sequence, also denoted as pilot symbols. As a result, a phase discrimination method using CPICH can be used. First, this known method estimates the phase variation between two consecutive pilot symbols. Then the frequency offset is obtained as the expectation of the following ratio:
                              f          o                =                  E          ⁡                      (                                          Δ                ⁢                                                                  ⁢                φ                                            Δ                ⁢                                                                  ⁢                T                                      )                                              (        1        )            
where:                Δφ stands for the phase variation between two consecutive pilot symbols,        ΔT is the inverse of the symbol rate, and        E( . . . ) denotes the expectation of the average function.        
Actually, to have an accurate estimation of the oscillator frequency offset, the previously described measurement needs to be repeated and averaged over a large number of pilot symbols. Consequently, the phase discrimination method is a long process triggered at the pilot symbol rate and which requires some time to have the local oscillator adjusted precisely.
On the other hand, due to radio receiver displacements, the frequency of the received radio signal is offset. This is known as the Doppler effect. As a consequence, for example, a high percentage of the baseband signal power in a power density spectrum lies in a frequency sub-range [−fd; fd], where frequency fd is the Doppler maximum frequency. Sub-range [−fd; fd] is known as the Doppler bandwidth.
For example, frequency fd is useful to estimate the wireless receiver speed.
It is known from “Non parametric Doppler Spread Estimation for Flat Fading Channels”, Kareem E. Baddour, Norman C. Beaulieu, IEEE 2003, that fd can be estimated as the frequency for which the signal power in the sub-range [−fd; fd] is equal to a certain percentage of the total signal power, as expressed by the following relation:
                                                        ∫                              -                                  f                  d                                                            f                d                                      ⁢                                                            P                  yy                                ⁡                                  (                  f                  )                                            ⁢                              ⅆ                f                                                                        ∫                                                -                                      f                    s                                                  /                2                                                              f                  s                                /                2                                      ⁢                                                            P                  yy                                ⁡                                  (                  f                  )                                            ⁢                              ⅆ                f                                                    >        ψ                            (        2        )            
where                ψ is an arbitrary constant power threshold belonging to ]0,1[        fs is the sampling frequency, and        Pyy(f) is an estimate of the signal power at frequency f.        
Pyy(f) is computed using FFT (Fast Fourier Transform) algorithm from the received baseband signal on a pilot channel like CPICH, for example.
However, the FFT-based fd estimation is not robust at all to oscillator frequency offset.
Usually, frequency fd and offset f0 are estimated independently, using two dedicated functional units.